Asians and Cash Dividends: Exploiting Symmetries in Pricing Theory

Centrum voor Wiskunde en Informatica, MAS Working Paper No. R0019

18 Pages Posted: 14 Aug 2000

See all articles by Jiri Hoogland

Jiri Hoogland

Centrum voor Wiskunde en Informatica (CWI)

Dimitri Neumann

Centrum voor Wiskunde en Informatica (CWI)

Date Written: June 26, 2000

Abstract

In this article we present new results for the pricing of arithmetic Asian options within a Black-Scholes context. To derive these results we make extensive use of the local scale invariance that exists in the theory of contingent claim pricing. This allows us to derive, in a natural way, a simple PDE for the price of arithmetic Asians options. In the case of European average strike options, a proper choice of numeraire reduces the dimension of this PDE to one, leading to a PDE similar to the one derived by Rogers and Shi. We solve this PDE, finding a Laplace-transform representation for the price of average strike options, both seasoned and unseasoned. This extends the results of Geman and Yor, who discussed the case of average price options. Next we use symmetry arguments to show that prices of average strike and average price options can be expressed in terms of each other. Finally we show, again using symmetries, that plain vanilla options on stocks paying known cash dividends are closely related to arithmetic Asians, so that all the new techniques can be directly applied to this case.

JEL Classification: G12, G13

Suggested Citation

Hoogland, Jiri and Neumann, Dimitri, Asians and Cash Dividends: Exploiting Symmetries in Pricing Theory (June 26, 2000). Centrum voor Wiskunde en Informatica, MAS Working Paper No. R0019. Available at SSRN: https://ssrn.com/abstract=234830 or http://dx.doi.org/10.2139/ssrn.234830

Jiri Hoogland

Centrum voor Wiskunde en Informatica (CWI) ( email )

P.O.Box 94079
MAS
NL-1090 GB Amsterdam
Netherlands
+31(20)5924102 (Phone)
+31(20)5924199 (Fax)

Dimitri Neumann (Contact Author)

Centrum voor Wiskunde en Informatica (CWI) ( email )

P.O.Box 94079
MAS
NL-1090 GB Amsterdam
Netherlands
+31(20)5924102 (Phone)
+31(20)5924199 (Fax)

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